New Directions in Mathematical Fluid Mechanics

The scientific interests of Professor A.V. Kazhikhov were fundamentally devoted to Mathematical Fluid Mechanics, where he achieved outstanding results that had, and still have, a significant influence on this field. This volume, dedicated to the memory of A.V. Kazhikhov, presents the latest contributions from renowned world specialists in a number of new important directions of Mathematical Physics, mostly of Mathematical Fluid Mechanics, and, more generally, in the field of nonlinear partial differential equations. These results are mostly related to boundary value problems and to control problems for the Navier-Stokes equations, and for equations of heat convection. Other important topics include non-equilibrium processes, Poisson-Boltzmann equations, dynamics of elastic body, and related problems of function theory and nonlinear analysis.

Preface	p. vii
Scientific Portrait of	p. ix
Boundary Control Problems for Stationary Equations of Heat Convection	p. 1
Homogenization of the Poisson-Boltzmann Equation	p. 23
Superconducting Vortices: Chapman Full Model	p. 41
Augmented Lagrangian Method and Compressible Visco-plastic Flows: Applications to Shallow Dense Avalanches	p. 57
Oscillatory Limits with Changing Eigenvalues: A Formal Study	p. 91
Finite-dimensional Control for the Navier-Stokes Equations	p. 105
On the Sharp Vanishing Viscosity Limit of Viscous Incompressible Fluid Flows	p. 113
Small Péclet Number Approximation as a Singular Limit of the Full Navier-Stokes-Fourier System with Radiation	p. 123
New Perspectives in Fluid Dynamics: Mathematical Analysis of a Model Proposed by Howard Brenner	p. 153
Existence of a Regular Periodic Solution to the Rothe Approximation of the Navier-Stokes Equation in Arbitrary Dimension	p. 181
Optimal Neumann Control for the Two-dimensional Steady-state Navier-Stokes equations	p. 193
On Some Boundary Value Problem for the Stokes Equations with a Parameter in an Infinite Sector	p. 223
Unilateral Contact Problems Between an Elastic Plate and a Beam	p. 237
On Lighthill's Acoustic Analogy for Low Mach Number Flows	p. 247
On the Uniqueness of Solutions to Boundary Value Problems for Non-stationary Euler Equations	p. 281
On Nonlinear Stability of MHD Equilibrium Figures	p. 301
Viscous Flows in Domains with a Multiply Connected Boundary	p. 333
Problems with Insufficient Information about Initial-boundary Data	p. 349
On the Stability of Non-symmetric Equilibrium Figures of Rotating Self-gravitating Liquid not Subjected to Capillary Forces	p. 379
Dynamics of a Non-fixed Elastic Body	p. 415
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New Directions in Mathematical Fluid Mechanics

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